Having fun with science and technology.

Moore's Law for Quantum Computers

By looking at the history of quantum computing experiments, one finds
an exponential increase in the number of qubits, similar to Moore's
law for classical computers. Quantum computing power doubles about
every six years, with quantum computers for real applications arriving
in between nine and twelve years if this trend continues.

The challenge of scalability in quantum computing remains an area of
vivid speculation in discussions both within the scientific community
and beyond it. Yet, to my knowledge, nobody has ever made an effort to
quantify the track record of the field. Such an empirical analysis
allows to make predictions that go beyond the usual saying that
practical quantum computers are "twenty years away".

Of course, if we wish to quantify things, we first have to specify the
rules of the game. Since we are interested in scalability, the natural
quantity of interest is the number of qubits realized in an
experiment. Second, experiments should demonstrate controlled coherent
manipulation of individual quantum objects, such as multi-qubit gates
or generation of mutual entanglement. This rules out, for example,
liquid state NMR ensemble realizations done with pseudopure states,
such as Ike Chuang's remarkable seven-qubit prime
fac­tor­i­za­tion
experiment. Finally,
"controlled manipulation" implies that entanglement is not merely
generated as a natural process, otherwise the Bell experiments going
back to Clauser in
1972 would count as a
two-qubit quantum computer. Alternatively, we could also say that we
look only at experiments with at least three qubits, as this is where
the real business starts. In any case, it is perfectly fine to use
such natural events as a resource for creating higher order entangled
states, as it is done in linear optics quantum computers. While there
is certainly some ambiguity with these definitions, they have only
little impact on the results.

Having established the rules to play by, the first experiment
fulfilling the criteria is the demonstration of the Cirac-Zoller
gate for two trapped
ions by Dave Wineland's group at NIST in 1995. In the following, the
number of qubits grew rapidly over the years, with ion trap
experiments and linear optics implementations competing for the top
spot. Currently, the world record in mutual entanglement is at
14 qubits,
demonstrated last year by Rainer Blatt's ion trap group in
Innsbruck. If we plot the progression of these records over time, we
obtain the following plot (if your browser supports SVG, clicking on a
data point will direct you to the respective publication):

As the qubit scale is logarithmic, this clearly corresponds to an
exponential increase, similar to Moore's law for classical
computers. The blue line is a fit to the data, indicating a doubling
of the number of qubits every 5.7±0.4 years. We can now use this
exponential fit to make some very interesting predictions.

Of course, we would like to know when we can expect quantum computers
to become superior to classical computers, at least for some
problems. The first real applications of quantum computers will come
in the area of simulating difficult quantum many-body problems
arising, for example, in high-temperature
su­per­con­duc­tiv­i­ty, quark bound states such as proton and
neutrons, or quantum magnets. For these problems, the record for
classical simulations is currently at 42
qubits. While
classical computers will see future improvements as well, a
conservative estimate is that you need to control 50 qubits in your
quantum computer to beat classical simulations. Extrapolating from our
exponential fit, we can expect this to happen between 2020 and
2023. Optimization and search problems benefiting from Grover's
algorithm could become tractable somewhat later, but that
depends a lot on the problem at
hand. If you are bold
enough to believe that the same scaling continues even further,
2048-bit RSA keys would come under attack somewhere between 2052 and
2059.

So, is this really going to happen? The current experiments are
limited by technical error sources, and theorists like myself are
constantly developing new ideas on how to deal with the fundamental
problems. And even if the current designs turn out to be not scalable
beyond a certain size, other architectures based on diamond
defect centers or
su­per­con­duc­ting
circuits are rapidly
catching up. My personal take is that the current exponential increase
could certainly last for another decade, making the estimate on
reaching 50 qubits by then sound realistic. However, whether the
quantum version of Moore's law will last as long as its classical
counterpart, is something that only time will tell.